Lemma 2.7 
Assume that a Bernstein-von Mises theorem is satisfied for a GFD, \(r_n(\theta | \mathbf {y})\) , such as in the result from [1]}:
\(\int _{\mathbb {R}^d} \left| r_n^*(s | \mathbf {y}) - \phi ^*_{0, I(\theta _0)}(s) \right| ds \overset{P_{\theta _0}}{\rightarrow } 0,\) 
